Java3D shapes to visad shapes?

Being too lazy to compute vertices and normals for the kinds of shapes I'd like 
to display,
 I'm trying to convert Java3D shapes (for which Sun has several nice ones built 
in, e.g. spheres)  
to VisAD shapes, and *almost* succeeding,  in that the shape (a sphere in this 
case) is recognizable
 but some of the vertexes are connected wrong.  It's close enough in appearance 
that I think it might 
be a small thing to fix though - hopefully somebody can spot what's wrong with 
this code:

 /*
 import javax.media.j3d.Appearance;
 import javax.media.j3d.GeometryArray;
 import com.sun.j3d.utils.geometry.Sphere;
 */
  
        // Get a Java3d shape
   Sphere sphere_j3d = new Sphere(1.0f, new Appearance());
   GeometryArray sphere_geom = 
(GeometryArray)sphere_j3d.getShape().getGeometry();
        
 VisADTriangleArray sphere = new VisADTriangleArray();
 sphere.vertexCount = sphere_geom.getValidVertexCount();
        
        float[] coords = new float[3*sphere_geom.getValidVertexCount()];
        float[] normals = new float[3*sphere_geom.getValidVertexCount()];
        float[] vec = new float[3];
        
        for (int i=0; i<sphere_geom.getValidVertexCount(); ++i)
        {
            sphere_geom.getCoordinate(i, vec);
            coords[3*i] = vec[0];
            coords[3*i + 1] = vec[1];
            coords[3*i + 2] = vec[2];
            
            sphere_geom.getNormal(i, vec);
            normals[3*i] = vec[0];
            normals[3*i + 1] = vec[1];
            normals[3*i + 2] = vec[2];
        }
        
        sphere.coordinates = coords;
        
        sphere.normals = normals;

 // ////////////////////////////////////////////////////////////        
 // This shorter way has the same effect

        //float[] sphere_vertexes = new float[3*sphere_geom.getVertexCount()]; 
        //sphere_geom.getCoordinates(0, sphere_vertexes);
        //sphere.coordinates = sphere_vertexes;
        
        //float[] sphere_normals = new float[3*sphere_geom.getVertexCount()];
        //sphere_geom.getNormals(0, sphere_normals);
        //sphere.normals = sphere_normals;